{
  "abstract": "This paper develops an embedded-hybridized discontinuous Galerkin (E-HDG) method combined with a first-order implicit-explicit scalar auxiliary variable (IMEX-SAV) time discretization for variational initial-state data assimilation governed by the unsteady incompressible Navier-Stokes equations. We adopt an optimize-then-discretize strategy. The spatial discretization uses discontinuous piecewise polynomials of degrees $k$ and $k-1$ for the element velocity and pressure, respectively, a continuous degree-$k$ velocity trace, and a discontinuous degree-$k$ pressure trace. The resulting state and adjoint velocities, as well as the reconstructed initial velocity, are globally divergence-free. The forward IMEX-SAV state scheme is unconditionally energy stable. Under suitable regularity and local-trajectory assumptions whose bounds introduce no explicit negative powers of the viscosity, the mesh-dependent condition $Δt\\lesssim h^2$, and a contractivity condition on the Tikhonov parameter, we establish local existence and uniqueness of the fully discrete OTD optimality system and Reynolds-semi-robust $L^2$ error estimates of order $O(h^k+Δt)$ for the state, adjoint and reconstructed initial velocities; the constants contain no explicit negative powers of the viscosity. Numerical experiments confirm convergence on smooth tests and demonstrate machine-precision discrete incompressibility, effective nonlinear-solver behavior, and stable performance in small-viscosity regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17096",
  "author_total": 3,
  "authors": [
    {
      "name": "Ya Min"
    },
    {
      "name": "Xian Zhang"
    },
    {
      "name": "Xiaoping Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r1dyagps0z10.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17096",
  "fulltext_url": null,
  "id": "2r1dyagps0z10",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17096",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.17096",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2r1dyagps0z10.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17096",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17096"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Reynolds-Semi-Robust, Globally Divergence-Free E-HDG/IMEX-SAV Method for Variational Initial-State Data Assimilation of the Navier-Stokes Equations",
  "title_text": "A Reynolds-Semi-Robust, Globally Divergence-Free E-HDG/IMEX-SAV Method for Variational Initial-State Data Assimilation of the Navier-Stokes Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/2r1dyagps0z10",
  "venue": "arXiv",
  "versions": []
}